…that are used to hold the glass in the dado.
The correct term is RABBET!
That applies to me, too, as I said I can make a 'groove,' when it's a rabbet, LOL.
Having settled that, any glass door will have some weight to it. Glass doors that tilt upwards will need to have the glass quite secure using a silicone bond in the rabbet. You don't want a loose pane that will rattle or drop out due to a failure of the fasteners. Gas piston door supports/struts will work to hold the door in a horizontal position. They will need to be appropriate for the weight of the door and width however, otherwise too much force will cause the frame to twist at the corners and possibly break the glass. Travel trailers and motor home often use tilt up doors for storage, check them out. A RV distributor may have the appropriate struts. RV shows are common in the early spring.
I'm going to go with regular plate glass; I think that's 1/8". (9 5/8" x 34 1/2", BTW) So I'm thinking it won't be too heavy. Nice tip on RV stuff. There's a dealer not too far from me. I'll stop by the next time I'm out.
It appears that your opening has a frame around it now. This means there is a ledge extending all around the opening which may catch on the object being placed inside or moved, so be cautious. There is apparently a door on the right side of this opening hinged with surface mount hinges. You may not be able to match those hinges in your application so check that out. The wood does appear to be Pine as I see what looks like a knot. The Pine looks to be clear with few if any knots, so use that for your new frame.
Yes, there's a frame there now. And a cabinet door on the right. Where the opening is now use to be cabinets with doors on them like the door on the right. They went down another foot or so. I had the bottom 'chopped' off to fit the 'new' fridge about 12 years ago. The space for the fridge was tiny, maybe for a 16 – 18 cu ft unit at best. I'll look locally for hinges. If I don't find any I'll go thru the 'gazillion' pages at Rockler.
If you take Toolmans suggestion, a good one, and use two hinged doors, that will solve some of the above issues, but there is another person's opinion which matters in this case.
Yeah… the boss', LOL. If it were just me, I'd go the two door route.